Challenge Yourself #CHAPTER3

A * H is a set of _____ coset.

a * H = H * a relation holds if __________.

A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called ____________.

An isomorphism of a group onto itself is called ____________.

The homomorphism of a group onto itself is defined as the ___________.

The elements of a vector space form a/an ____________ under vector addition.

A set of representatives of all the cosets is called _________.

Which of the following statement is true?

How many different non-isomorphic Abelian groups of order 8 are there?

Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________.